Temperature and concentration dependence of k p

As is known from other water-soluble monomers such as acrylic acid (AA)^[104], methacrylic acid (MAA)^[114], prop-2-enamides^[71], N-vinyl pyrrolidone^[73] and N-vinyl formamide^[107], the solvent water has an significant influence on the propagation rate coefficient, kp, the Arrhenius parameter A⁰, the pre-exponential factor, and a weaker effect on E^A, the activation energy. These studies showed that k^p and A⁰ increase toward lower monomer concentration.

To quantify the influence of the water concentration and the temperature on PEGMA polymerization, the k^p data were determined ranging from PEGMA bulk toward 90 wt% H²O at 22, 30, 40, 60 and 80 °C. The water dependency will also be correlated to the structural aspects of PEGMA.

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The first part of this subchapter deals with the estimate of A0 and EA

for PEGMA in bulk. A0 and EA are obtained via the Arrhenius-relationship of k^p. The absolute k^p values and their dependency on water content will be discussed in the second part of this section.

The Arrhenius plots for different monomer concentrations are shown in Figure 3.3. Although these Arrhenius plots in Figure 3.3 show some scattering and indicate that the activation energy is slightly higher at lower temperatures, the kp data have been fitted with a single straight line for each solvent composition. All data points exhibit a linear dependency and may therefore be represented by linear fits. The following discussion focuses on the Arrhenius parameter for bulk PEGMA, which is represented by the black line.

For PEGMA in bulk an EA of 22 kJ mol⁻¹ has been estimated. This value is in a good agreement with other methacrylate type monomers, e.g., methyl methacrylate (MMA), butyl methacrylate (BMA) and dodecyl methacrylate (DMA), and indicates a certain family behavior.^[97,100]

Depicted in Table 3.2 are E^A, A⁰ and k^p values at 25 °C for different water-soluble methacrylic monomers, such as MAA, 2-hydroxyethyl methacrylate (HEMA) and PEGEEMA. Except for MAA, each monomer exhibits an E^A in the range of 22 kJ mol⁻¹ in bulk which agrees with the hydrogen-bonded interactions.^[72,114] All other examples of water-soluble monomers have an ester functionality which may interact only to a weaker extent with the radical functionality of the propagating radical.

The fact that the monomer interacts with the radical functionality may also influence the vibrational and rotational motion in the transition state for propagation. For this reason it seems worthwhile to compare the second Arrhenius parameter, A0, which is linked to the mobility of the radical, for PEGMA with the other monomers in Table 3.2.

0.0028 0.0029 0.0030 0.0031 0.0032 0.0033 0.0034 6.0

6.5 7.0 7.5 8.0 8.5 9.0

100 wt.% PEGMA 50 wt.% PEGMA 30 wt.% PEGMA

ln(k p / (L mol1 s1 ))

T^1 / K^1

23 2 kJ mol^1

19 2 kJ mol^1

22 2 kJ mol^1

Figure 3.3: Variation of kp for PEGMA with temperature and three different monomer mass fractions in aqueous solution. The straight lines represent an Arrhenius fit.

The A0 values in Table 3.2 are varying by one order of magnitude from A0 = 0.4 ∙ 10⁶ L mol⁻¹ s⁻¹ for MAA to A0 = 8.9 ∙ 10⁶ L mol⁻¹ s⁻¹ for HEMA. A⁰ for PEGMA lies in the middle of these values at 3.5 ∙ 10⁶ L mol⁻¹ s⁻¹ which is not surprising, as MAA and HEMA are monomers with special properties.

The very small A⁰ for MAA might be explained by the carboxylic acid group of MAA. The carboxylic acid group is known to strongly interact with other MAA molecules, as is shown by the spectroscopic detection of cyclic MAA dimers.^[115] For this reason, it is expected that MAA in bulk exhibits a high barrier for internal rotational motion of the transition state and thus A⁰ is strongly reduced.^[75]

On the contrary, HEMA is a carboxylate ester with a hydroxyethyl group. The ester group and the short side chain may weakly interact

36

Table 3.2: Activation energies, Arrhenius pre-exponential factors and k^p -values at 25 °C for different methacrylic monomers in bulk.

E^A / kJ mol⁻¹

A⁰ / (10⁶ L mol⁻¹ s⁻¹)

k^p / L mol⁻¹ s⁻¹

Methacrylic acid^[75,106] 16 0.4 600

2-Hydroxyethyl

Besides the almost identical poly(ethylene glycol) side chain, PEGMA and PEEGEMA are distinguished by a shorter poly(ethylene glycol) side chain for PEGEEMA. Because of the shorter side chain, it is expected that the rotational mobility of the radical functionality is increased, and thus results in a higher A⁰. It should be noted that E^A and A⁰ are correlated with each other and a higher estimated E^A for PEGEEMA may yield accordingly a higher A⁰.

Since the vibrational and rotational motions of the transition state 23 kJ mol⁻¹, respectively (see also Table 3.3). As shown in Figure 3.3, kp

increases additionally with the water content.

To check the quality of the Arrhenius plots, 95% joint confidence intervals (JCIs) were estimated for the measured concentration range.

Depicted in Figure 3.4 are JCIs corresponding to the Arrhenius plots in

0 5 10 15 20 25 18

19 20 21 22 23 24 25

EA / (kJ mol1 )

A0 / (10⁶ L mol^1 s^1) bulk

50 wt.-% PEGMA 30 wt.-% PEGMA

Figure 3.4: 95 % joint confidence region for the Arrhenius parameters of k^p for PEGMA for various monomer mass fractions in aqueous solution. The symbols (X) indicate the best estimates of Arrhenius activation energy and pre-exponential factor.

Figure 3.3. These JCIs were obtained by a nonlinear least-squares fit assuming a constant error of kp as suggested by van Herk.^[116] The JCIs are not overlapping, however regarding the experimental uncertainty of ΔE^A = ± 2 kJ mol⁻¹ it may be justified to assume that the activation energy is independent of monomer concentration, and EA = 21 kJ mol⁻¹. This behavior has also been observed for MAA, various acrylamides and AA at high monomer concentrations, those activation energies are also independent of monomer concentration.[71,104,114]

EA being independent of the water concentration indicates that H2O has no effect on the reaction barrier of the propagating radicals of PEGMA and thus the increase in k^p is not induced by lowering the reaction barrier. Considering the absence of hydrogen-bonded interactions of PEGMA with itself and with the aqueous environment it

38

could be expected that water has no effect on the reaction barrier. For MAA is has been reported that hydrogen-bonded interactions with water molecules appear to have an almost identical effect on the reaction barrier as MAA molecules.^[114]

Since an increase in kp may not be induced by a change of EA, another fact that needs to be discussed is the impact of water content on A⁰. Shown in Figure 3.5 are the estimated A⁰ values for bulk, 50 and 30 wt% under the assumption that EA is constant at 21 kJ mol⁻¹. From bulk to 50 and 30 wt% PEGMA/H2O A0 increases in a linear fashion by a factor 4 from 3.5 to 9.3 and 14.4 ∙ 10⁶ L mol⁻¹ s⁻¹, respectively.

Listed in Table 3.3 are the estimated A0 and associated kp values at 25 °C for bulk, 50 and 30 wt% PEGMA in water. Although an increase in A0 with the water concentration is associated with an increased kp, the kp

values exhibit an increase only by a factor of 3 instead of a factor 4 as it was found for A⁰. However, this increase is still consistent with the previously discussed theory of a better rotational motion and thus a higher kp.

The same behavior has been observed for MAA in water. In contrast to PEGMA, A0 for MAA exhibits a stronger increase, by one order of magnitude, from bulk A0 = 4.0 ∙ 10⁵ L mol⁻¹ s⁻¹ toward A⁰ = 3.64 ∙ 10⁶ L mol⁻¹ s⁻¹ at 5 wt% MAA.^[75,114] It should be noted that due to the high molar mass of PEGMA the concentration of 30 wt% PEGMA correspond to 0.57 mol ∙ L⁻¹, whereas 5 wt% MAA in water compares to 0.59 mol ∙ L⁻¹ which is almost the same molar monomer concentration.

Shown in Figure 3.6 is a semi-logarithmic plot for the A⁰-values of PEGMA and MAA versus monomer concentration at 20 °C. A⁰ was calculated from the kp values extracted from Figure 3.7 below with the approximation of EA being independent of monomer concentration. The A⁰ values for PEGMA are by one order of magnitude above the ones for MAA bulk. At infinite dilution, the difference is reduced to a factor of 4.

A0 for PEGMA increases in a linear fashion from bulk toward highly diluted aqueous solutions. On the contrary, the water dependence of A⁰ for MAA may follow an exponential course. Between 50 wt% and bulk MAA the increase in A⁰ is almost identical to the one for PEGMA. At higher water concentration above 50 wt% the increase in A0 for MAA is more pronounced.

0 10 20 30 40 50 60 70 80 90 100 10⁶

10⁷

A0 / L mol1 s1

c_PEGMA / wt%

Figure 3.5: Variation of A⁰ for PEGMA with the water content. The A⁰ are obtained from the Arrhenius plot of Figure 3.3 under the assumption that E^A is constant at 21 kJ mol⁻¹. The straight lines represent the best fit (the results are replicated in Table 3.3).

Table 3.3: Arrhenius parameter and kp for PEGMA at 25 °C for various PEGMA/H²O mixtures.

wt% PEGMA 100 50 30

E^A / kJ mol⁻¹ 21 ± 2 21 ± 2 21 ± 2

A0 / (10⁶ L mol⁻¹ s⁻¹) 2.1 ≤ 3.5 ≤ 8.0 5.9 ≤ 9.3 ≤ 10.7 6.2 ≤ 14.4 ≤ 23.0 k^p(25 °C) / L mol⁻¹ s⁻¹ 500 1400 1700

The stronger water dependency of A⁰ for MAA might be explained by the carboxylic moiety which allows for stronger intermolecular interactions through hydrogen bonds and dipole-dipole interactions.

40

0 20 40 60 80 100

10⁶ 10⁷

PEGMA MAA

A0 / L mol1 s1

cmonomer / wt%

Figure 3.6: Variation of A⁰ with monomer concentration in aqueous solution for MAA and PEGMA at 20 °C. A constant EA for MAA and PEGMA were used with 16 kJ mol⁻¹ for MAA and 21 kJ mol⁻¹ for PEGMA.

For bulk polymerization, the interactions of MAA may be stronger with the propagating center. This leads to a more pronounced retardation of k^p. Upon replacing MAA by H²O molecules in the direct vicinity of the propagating center at high dilution, the interaction of water molecules weakens the influence of MAA molecules on the propagating center and result in a better internal rotational freedom of the radical functionality.^[106]

PEGMA, on the contrary, bears a very weak proton acceptor side chain with weak dipole-dipole interactions. This leads to a small hindrance of the internal rotational mobility. The fluidizing effect of water is less pronounced for monomers with a high mobility even in bulk.

As described above, A⁰ increases with the water content and that E^A is independent of the H²O concentration. The next part focusses on the water dependency of k^p in correlation with the obtained Arrhenius parameters.

The k^p values in bulk of various water-soluble methacrylates show a

correlation between A0 and kp. The kp values for different water-soluble methacrylates such as MAA, HEMA and PEGEEMA in bulk at 25 °C are listed in Table 3.2. The structure of PEGEEMA and PEGMA is almost identical, therefore the k^p values are very similar with 490 L mol⁻¹ s⁻¹ for PEGEEMA and 500 L mol⁻¹ s⁻¹ for PEGMA.^[109]

For HEMA, a much higher k^p value of 1200 L mol⁻¹ s⁻¹ was obtained than for PEGMA.^[99] The relatively high kp in bulk may be explained by the short alcoholic side chain, which provides a small dipole-dipole moment and thus a weak hindrance to internal rotational mobility. This is also reflected in the high A⁰ value.

Although MAA exhibits the smallest A⁰ from the listed monomers the k^p value is slightly higher than for PEGMA due to the lower activation energy.

After discussing the differences of k^p in bulk, the change of k^p with monomer concentration is of interest, since the evolution of kp with monomer concentration varies with the type of monomer.[71,76,114] The comparison focus on MAA and PEGMA. The already investigated water-soluble amides are not considered here because they represent a completely different monomer family.

From the right column of Table 3.1 the following conclusion can be drawn: kp is strongly decreasing from highly diluted solutions of PEGMA, kp = 3200 L mol⁻¹ s⁻¹, toward bulk polymerization, k^p = 500 L mol⁻¹ s⁻¹. Shown in Figure 3.7 is the variation of k^p over the entire concentration range for PEGMA and MAA in aqueous solution at 20 °C.

The data for PEGMA plotted in Figure 3.7 were fitted with the following expression:

𝑘_𝑃/ (L mol⁻¹s⁻¹) = 5643 − 1086 ∙ ln (𝑐_PEGMA/(wt%) + 5.989) (3.1)

As seen in Figure 3.7, k^p increases toward lower monomer concentration. The propagation rate coefficient of PEGMA increases by a factor of 7 from bulk, k^p = 500 L mol⁻¹ s⁻¹, toward infinite dilution, kp ≈ 3700 L mol⁻¹ s⁻¹. For methacrylic acid (MAA) a stronger increase by a factor 13 of k^p has been observed from bulk, k^p = 600 L mol⁻¹ s⁻¹, toward

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Figure 3.7: Variation of kp with monomer concentration for polymerizations of PEGMA in water with different initiator concentration at 22°C.

infinite dilution, kp ≈ 7500 L mol⁻¹ s⁻¹. This increase in kp becomes more pronounced in highly diluted solutions of PEGMA and MAA. PEGMA shows an almost linear increase in k^p from bulk toward 30wt% PEGMA, whereas MAA shows a very weak increase in kp above 60 wt%. For higher dilutions, the increase in kp is more pronounced for both monomers. The increase in k^p for MAA is however significantly stronger than for PEGMA. The stronger water influence at higher dilution is the transition state for propagating radical is less hindered and that the

fluidizing effect of water is less pronounced for monomers with high A0

values in bulk.

Im Dokument Cu- and Fe-mediated Atom-Transfer Radical Polymerization in Aqueous Solution (Seite 41-51)